![]() Use tape to secure large sheets of paper to the floor for the robot drawing.Construct and program the LEGO EV3 robot, as provided in The Fibonacci Sequence & Robots activity.Using the Squares Puzzle Template, cut and laminate poster board pieces, labeling the size on each piece, making enough for one puzzle per group.Print out and laminate enough copies of the three-page Natural Pictures document so that each group can have at least one picture at any given time. ![]() Gather materials and make copies of the Brainstorming Squares, and Math Adventurers Worksheet (one each for every two students). ![]() Today, we are also going to program a robot to follow the phi ratio and see what happens. How did the robot follow your orders (the program) when completing the Fibonacci sequence? Did the robot exactly follow your orders? How precise did you have to be with your programming for the robot? (Expect students to be able to recognize that the robot does only exactly what is it told to do it is incapable of making addition errors, for example.) This type of precision is necessary by engineers when programming robotic technologies, such as robotic arms used in foundries or surgeries. (Assuming you have conducted the companion activity, The Fibonacci Sequence & Robots.) Now, let's think about the robots that we have programmed with the Fibonacci sequence. It turns out that the ratio of successive terms of the Fibonacci sequence is phi. Next, you will think about how these rectangles relate to each other. In the squares puzzle part of this activity, you can solve this puzzle in a variety of ways by making increasingly larger rectangles with side lengths terms of the Fibonacci sequence. (If necessary, use the classroom board or an overhead projector to show students how to generate the next terms.) If I begin with 0 and 1, who can tell me the next few numbers in the sequence? (Answer: 1, 2, 3, 5.) The mathematical source of phi, the Fibonacci sequence, is a sequence formed by adding two successive terms to get the next term. (right) Glenlarson, Wikipedia (US PD) ĭuring today's activity, you will "discover" phi in two ways: through a simulation and through examination of specific mathematical objects. The "Golden Ratio," phi, based on the Fibonacci sequence, can be seen in nature in the spiral of shells, and in the pleasing proportions of archectural designs, such as the ancient Parthenon in Athens, Greece.Ĭopyright © (left) 2004 Microsoft Corporation, One Microsoft Way, Redmond, WA 98052-6399 USA. Also, phi has been observed in many areas of mathematics, from geometry such as regular pyramids, to number theory, such as Lagrange's approximation theorem. Phi, as a ratio, features prominently in works of da Vinci and Dali. And, it plays a key role into Western aesthetics and architecture. It is found all over in nature, from snail shells and flower seed heads to many plant patterns such as those in pineapples, ferns and pinecones. The formalization of phi may have been motivated by its presence in the pentagram, a common religious symbol at that time. The mathematical constant phi has been studied since at least 300 BCE, when it was defined by Greek mathematician Euclid. International Technology and Engineering Educators Association - Technologyįibonacci Sequence Robot MINDSTORMS NXT Program (rbt) Visit [ to print or download.Ībility to perform division, and an understanding of the basic concept of a function. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Investigate patterns of association in bivariate data. Use ratio reasoning to convert measurement units manipulate and transform units appropriately when multiplying or dividing quantities. Identify phi as the limit of the ratio of terms of the Fibonacci sequence.įluently divide multi-digit numbers using the standard algorithm.įluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.Explain the general term of the Fibonacci sequence.This activity builds upon the omnipresence of this number to introduce students to discrete mathematics, and extends the idea of a mathematical sequence to basic programming using the EV3 MINDSTORMS software.Īfter this activity, students should be able to: In art, this constant is used to quantify aesthetic beauty, such as in da Vinci's Mona Lisa, or even the face of a beautiful person. ![]() From the great pyramids to the Parthenon, this number appears in the shapes and scales of many engineering designs and architectural feats. Phi is arguably one of the most important mathematical constants. ![]() Copyright © (left) 2008 User:Dicklyon, Wikipedia (PD) and (right) 2007 Karora, Wikimedia (PD) ![]()
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